Writing and Printing

Decimal

A decimal system (also called base-ten, denary or decenary) is a numeral system that uses ten as its radix (base). Decimal systems are the global standard for denoting integer and non-integer numbers. The way of denoting numbers in a decimal system is often referred to as decimal notation. Presently, the most common decimal system is the Hindu–Arabic numeral system, which is a positional numeral system. However, there are also non-positional base-ten systems, such as Roman or Chinese numerals. A decimal numeral (also often just decimal or, less correctly, decimal number), generally refers to the notation of a number in a decimal numeral system. Non-integral decimals may be identified by a decimal separator (usually "." or "," as in 25.9703 or 3.1415). In English, the word decimal often refers to the digits after the decimal separator, for example, that "3.14 is the approximation of π to two decimals" or "two decimal places." The numbers that may be represented exactly by a decimal of finite length are the decimal fractions. That is, fractions of the form a/10n, where a is an integer, and n is a non-negative integer. Decimal fractions also result from the addition of an integer and a fractional part; the resulting sum sometimes is called a fractional number. Decimals are commonly used to approximate real numbers. By increasing the number of digits after the decimal separator, one can make the approximation errors as small as one wants, when one has a method for computing the new digits. In the sciences, the number of decimal places given generally gives an indication of the precision to which a quantity is known; for example, if a mass is given as 1.32 milligrams, it usually means there is reasonable confidence that the true mass is somewhere between 1.315 milligrams and 1.325 milligrams, whereas if it is given as 1.320 milligrams, then it is likely between 1.3195 and 1.3205 milligrams. The same holds in pure mathematics; for example, if one computes the square root of 22 to two digits past the decimal point, the answer is 4.69, whereas computing it to three digits, the answer is 4.690. The extra 0 at the end is meaningful, in spite of the fact that 4.69 and 4.690 are the same real number. In principle, the decimal expansion of any real number can be carried out as far as desired past the decimal point.

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See also

• ▸Borama
• ▸Geography of Taiwan
• ▸Chu Sigyŏng

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